1. Field of the Invention
The present invention relates to modeling a workspace and, more particularly, to modeling the workspace of a device according to internal and external constraints.
2. Discussion of Related Art
Deformable models have been implemented in computer graphics and animation, in surgery simulation (deformable tissues), and in medical imaging (model-based segmentation). However, no known system or method exists for modeling the mechanical details and bending characteristics of an endoscope and the calculation of its workspace.
A model of an endoscope has been described as a part of a virtual endoscope system and method with force sensation. The model includes a collection of rigid links, interconnected by joints. To achieve real-time simulation, a simplified Newton-Euler equation of motion can be used. The simplified Newton-Euler equation disregards velocity and acceleration. A small number of joints are used as part of the virtual endoscope system, with increasing length from the endoscope tip to the head, which limits the accuracy of the model. Since the method is a simulator, for educational purposes, the emphasis is more on visual and palpable correctness than on millimeter accuracy.
Another method proposes a deformable model for long, thin instruments like catheters. A snake approach has been used. The shape of the catheter is represented by a fourth order B-spline, the control points of the B-spline are moved in an optimation process, to find a minimum energy representation.
One limitation of these models is that the special mechanics of the endoscope bending section have not been taken into account. Thus, the accuracy of the model can be difficult to maintain.
Therefore, a need exists for a method of modeling the internal and external constraints of a flexible endoscope for determining a workspace.